The Riemann hypothesis remains an unsolved problem in mathematics1. It is considered one of the most important unsolved problems in pure mathematics and has significant implications for number theory, particularly regarding the distribution of prime numbers1.

The Riemann hypothesis states that:

The real part of every non-trivial zero of the Riemann zeta function is 1/21.

In other words, all the non-trivial zeros of the Riemann zeta function lie on the critical line in the complex plane where the real part is 1/21.

Key points about the Riemann hypothesis:

1. It was proposed by Bernhard Riemann in 18591.

2. It is one of the Millennium Prize Problems, with a $1 million reward for its solution1.

3. The hypothesis has profound implications for the distribution of prime numbers1.

4. If proven true, it would provide the best possible bound for the error of the prime number theorem1.

5. Many mathematicians have attempted to prove or disprove it, but it remains unresolved1.

6. The hypothesis is equivalent to several other mathematical statements, including some about the regularity of the Farey sequence and bounds on certain arithmetic functions1.

Despite claims of proofs over the years, including a recent attempt by a renowned mathematician4, the mathematical community remains skeptical, and the Riemann hypothesis is still considered unsolved. Any claimed solution would require rigorous peer review and verification by the mathematical community before being accepted as valid.